General Optimized Lower and Upper Bounds for Discrete and Continuous Arithmetic Asian Options

Mathematics of Operations Research, 2016, 41(2), 531-559

37 Pages Posted: 4 May 2016 Last revised: 6 May 2016

See all articles by Gianluca Fusai

Gianluca Fusai

Università del Piemonte Orientale Dipartimento di Studi per l'Economia e l'Impresa; Sir John Cass Business School - City, University of London

Ioannis Kyriakou

City University London - Sir John Cass Business School

Abstract

We propose an accurate method for pricing arithmetic Asian options on the discrete or continuous average in a general model setting by means of a lower bound approximation. In particular, we derive analytical expressions for the lower bound in the Fourier domain. This is then recovered by a single univariate inversion and sharpened using an optimization technique. In addition, we derive an upper bound to the error from the lower bound price approximation. Our proposed method can be applied to computing the prices and price sensitivities of Asian options with fixed or floating strike price, discrete or continuous averaging, under a wide range of stochastic dynamic models, including exponential Lévy models, stochastic volatility models, and the constant elasticity of variance diffusion. Our extensive numerical experiments highlight the notable performance and robustness of our optimized lower bound for different test cases.

Keywords: arithmetic Asian options, CEV diffusion, stochastic volatility models, Lévy processes, discrete average, continuous average

Suggested Citation

Fusai, Gianluca and Kyriakou, Ioannis, General Optimized Lower and Upper Bounds for Discrete and Continuous Arithmetic Asian Options. Mathematics of Operations Research, 2016, 41(2), 531-559. Available at SSRN: https://ssrn.com/abstract=2774881

Gianluca Fusai

Università del Piemonte Orientale Dipartimento di Studi per l'Economia e l'Impresa ( email )

Via Perrone, 18
Novara, 28100
Italy

HOME PAGE: http://https://upobook.uniupo.it/gianluca.fusai

Sir John Cass Business School - City, University of London ( email )

106 Bunhill Row
London, EC2Y 8HB
Great Britain

HOME PAGE: http:// www.cass.city.ac.uk/experts/G.Fusai

Ioannis Kyriakou (Contact Author)

City University London - Sir John Cass Business School ( email )

Faculty of Actuarial Science & Insurance
106 Bunhill Row
London, EC1Y 8TZ
United Kingdom
+44 (0)20 7040 8738 (Phone)
+44 (0)20 7040 8881 (Fax)

HOME PAGE: http://www.cass.city.ac.uk/experts/I.Kyriakou

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